Comparison of two calculation methods of the optimal switching instants of a hybrid dynamic system

Two calculation methods of the optimal switching instants of a hybrid dynamic system are presented. The control problem is set as a minimization problem of the deviation between the state and a desired state, at the final instant. The first method uses the Lagrangian technique to calculate the gradient of a cost function and implements the Fletcher-Reeves descent method (Minoux, 1983). The second method is based on interval analysis. The set inversion algorithm SIVIA (Jaulin and Burger, 1999) which is presented and implemented, ensures guaranteed results. Both methods are applied to an example then compared